On the structure of the solution set of evolution inclusions with Fréchet subdifferentials

[摘要] In this paper we consider a Cauchy problem in which is present an evolution inclusion driven by the Fréchet subdifferential o∂−fof a functionf:Ω→R∪{+∞}(Ωis an open subset of a real separable Hilbert space) having aφ-monotone . subdifferential of order two and a perturbationF:I×Ω→Pfc(H)with nonempty, closed and convex values.First we show that the Cauchy problem has a nonempty solution set which is anRδ-set inC(I,H), in particular, compact and acyclic. Moreover, we obtain a Kneser-type theorem. In addition, we establish a continuity result about the solution-multifunctionx→S(x). We also produce a continuous selector for the multifunctionx→S(x). As an application of this result, we obtain the existence of solutions for a periodic problem.

[学科分类] 应用数学